Delay Analysis of Reservation Based Random Access: A Tandem Queue Model

Massive access has attracted considerable recent attention because it holds the promise of efficiently enabling connections of extensive devices in machine-type communications. A large portion of massive access protocols exploit the reservation-based mechanisms that can satisfy random access requests while avoiding much bandwidth waste due to packet collisions. In this paper, we present a unified framework based on a tandem queue model for analyzing and optimizing reservation-based random access protocols with arbitrary collision resolution methods. More specifically, the two queues characterize the channel reservation and packet transmission respectively. We present the high-dimensional Markov chain of the tandem queue, the transition matrix of which can be derived from arbitrary collision resolution algorithms. The transition matrix then allows us to calculate the average packet delay by solving a linear equation. To provide further insights, a typical reservation based access using tree splitting for collision resolution is analyzed from both theoretical and numerical perspectives.